It’s high intrigue and plenty of scheming in this Danish royalty piece set in the 18th century, with Alicia Vikander as a crafty princess who conspires with, and falls for, her husband’s doctor, Mads Mikkelsen.

The movies have always loved royalty, and why not? There’s pageantry galore, arranged marriages (as well as doomed extramarital love stories) and often some sort of madman near the throne or, in the case of Danish director Nikolaj Arcel’s “A Royal Affair,” actually occupying it.

Based on an 18th-century episode little known to most Americans, the film opens as English princess Caroline (Alicia Vikander) marries King Christian of Denmark (Mikkel Boe Folsgaard). But Christian is paranoid, sex-obsessed and, even more alarming, a frustrated actor. Caroline quickly grows to detest her husband but still manages to produce an heir.

Meanwhile, the forces of reform in Denmark finagle the liberal-minded Struensee (Mads Mikkelsen) into a position as the poor mad king’s doctor. Struensee rapidly gains favor with the king, and Caroline falls in love with the doctor. Together Struensee and Caroline push Christian to introduce a flood of reforms, from smallpox vaccinations to forbidding nobles to torture the peasants. Naturally the peasant-torture lobby pushes back, most notably Dowager Queen Juliane (Trine Dyrholm, so magnificently evil you expect her to offer Caroline a poisoned apple).

The narrative is a bit overstuffed, like cramming for an 8 a.m. pop quiz over morning coffee. There’s too much politics sharing the screen with nicely lit hanky-panky, as characters discuss Denmark’s economy with a precision that might make Paul Krugman glaze over.

Vikander’s innocent qualities play well for the first half-hour, less so later when the script calls for womanly depth and not dewy girlishness. Mikkelsen, whose Struensee never acquires a good suit nor a comb no matter how high he ascends, is better, deftly showing the change from modest plotter to power-wielding king in all but name.

“A Royal Affair” is basically a good-looking set of historical Cliffs Notes. There, is however, one excellent reason to see it: Folsgaard, who by the end has made his betrayed and bereft Christian into a figure of genuine tragedy.